How to Find the Area of a Circle Using Radius

By Hannah Richardson; Updated April 24, 2017

To find the area of a circle, you take pi times the radius squared, or A = pi r^2. Using this formula, you can find the area of a circle if you know the radius -- or the diameter -- by plugging in your values and solving for A. Pi is approximated as 3.14.

Whole Numbers

To find the area of a circle given the radius, plug in the value of the radius to the formula A = pi r^2. To do this, first you square the radius, then you multiply the result by pi. If the radius of your circle is 2, write out of your formula using 2 instead of r: A = pi (2)^2. After you square 2, your formula will be A = pi (4). If you use the pi button on your calculator, your answer will be A = 12.57, rounded to the nearest hundredth. If you use the approximation 3.14 for pi, your answer will be A = 12.56 exactly.

Decimals

The process is the same no matter how complicated your radius may seem. Even if you have a radius of 5.68412, you can still plug that number into the formula and square it. Your formula would then be: A = pi (32.30922017). Unless you have specific directions otherwise, don't round your answer until have multiplied by pi. Leaving everything on your calculator screen, multiply by pi, then round. If you use the pi button, your answer will be 101.50, rounded to the nearest hundredth. If you use the approximation 3.14, your answer will be 101.45.

Diameter

Even if you're given the diameter of a circle, you can still find the area of a circle using the radius. The radius is one half the diameter, so to get the radius, divide the diameter by 2, plug in the result and solve. If you have a diameter of 16, your radius is 8. Square 8 to get 64, then multiply by pi: A = pi x 64. This gives you an area of 201.06.

Fractions

No matter what your diameter looks like, you will still divide the diameter in half to find the radius. If your diameter is a fraction, such as 5/9, use properties of fractions to write it with a numerator divisible by two, and then divide. The fraction 5/9 becomes 10/18, and the radius is 5/18. Square 5/18 to get 25/324 by squaring the top and bottom of the fraction. Your formula becomes A = pi (25/324). Simplified, your answer is A = 0.24, rounded.

References

About the Author

Hannah Richardson has a Master's degree in Special Education from Vanderbilt University and a Bacheor of Arts in English. She has been a writer since 2004 and wrote regularly for the sports and features sections of "The Technician" newspaper, as well as "Coastwach" magazine. Richardson also served as the co-editor-in-chief of "Windhover," an award-winning literary and arts magazine. She is currently teaching at a middle school.